On two systems of Burgers type arising in nonlinear wave interaction
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912074963091456 |
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| author | Alonso-Orán, Diego Granero-Belinchón, Rafael |
| author_facet | Alonso-Orán, Diego Granero-Belinchón, Rafael |
| contents | In this note we study the well-posedness of two systems of Burgers type arising in nonlinear wave interactions. The first model describes the interaction of a Burger's bore with the classical Korteweg-de Vries equation while the second exemplify the interaction of weak sound waves and entropy waves with small amplitudes. For the former, we show the local existence and uniqueness of solutions in Sobolev spaces and Wiener-type spaces. For the latter, we provide an elementary proof of finite time singularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_11017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On two systems of Burgers type arising in nonlinear wave interaction Alonso-Orán, Diego Granero-Belinchón, Rafael Analysis of PDEs Mathematical Physics In this note we study the well-posedness of two systems of Burgers type arising in nonlinear wave interactions. The first model describes the interaction of a Burger's bore with the classical Korteweg-de Vries equation while the second exemplify the interaction of weak sound waves and entropy waves with small amplitudes. For the former, we show the local existence and uniqueness of solutions in Sobolev spaces and Wiener-type spaces. For the latter, we provide an elementary proof of finite time singularity. |
| title | On two systems of Burgers type arising in nonlinear wave interaction |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2410.11017 |